# Borel set, criterion for a

From Encyclopedia of Mathematics

A necessary and sufficient condition for an $\mathcal{A}$-set in a complete separable metric space to be a Borel set. Two criteria can be stated as follows: 1) its complement must also be an $\mathcal{A}$-set (Suslin's criterion); and 2) it can be represented as the union of non-intersecting components (Luzin's criterion).

**How to Cite This Entry:**

Borel set, criterion for a.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Borel_set,_criterion_for_a&oldid=35729

This article was adapted from an original article by A.G. El'kin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article